Exercise 1: Euler Algorithm Model of a SHO Build a computational model of a simple hanging harmonic oscillator using the Euler method with MATLAB. Use realistic values for the parameters (i. e., spring constant k and attached mass m) such as would be encountered in a typical introductory mechanics laboratory exercise. Also, assume that the mass of the spring is negligible compared to the attached mass, and that the harmonic oscillator has been stretched vertically downward a distance y0, relative to its hanging equilibrium position and released from rest. Use the model to produce graphs of the position and velocity of the mass as a function of time, and compare these with the exact functions for the position and velocity, y(t) = y0 cos   s k m t   and v(t) = − s k m y0 sin   s k m t   , 1 that result from solving Newton’s 2nd Law analytically. Does the angular frequency match that expected for a simple harmonic oscillator of mass m an spring constant k?